In the effective Ising spin-1/2 antiferromagnetic chain system BaCo2V2O8, the magnetic-field influence is highly anisotropic. For magnetic fields along the easy axis c, the Néel order is strongly suppressed already for low fields and an incommensurate order is entered above 4 T. We present a detailed study of the magnetic phase diagrams for different magnetic field directions, which are derived from magnetization data, high-resolution thermal expansion and magnetostriction measurements as well as from the thermal conductivity. Zero-field thermal expansion data reveal that the magnetic transition is accompanied by an orthorhombic distortion within the ab plane. Under ambient conditions the crystals are heavily twinned, but the domain orientation can be influenced either by applying uniaxial pressure or a magnetic field along the [100] direction. In addition, our data reveal a pronounced in-plane magnetic anisotropy for fields applied within the ab plane. For H [110], the magnetic field influence on TN is weak, whereas for magnetic fields applied along [100], TN vanishes at about 10 T and the zero-field Néel order is completely suppressed as is confirmed by neutron diffraction data. The second-order phase transition strongly suggests a quantum critical point being present at H 10 T parallel [100], where the Néel order probably changes to a spin-liquid state. The magnetization has been measured in a vibrating sample magnetometer (PPMS, Quantum Design) for temperatures above 2 K up to a maximum magnetic

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